For example if silver is at 12.82 with three months to expiration I buy a call $4 away from the money how much will this option increase if the price of silver increase by $3.

Or how much will the price of an option increase if silver jumps $1.50 in one week.

I'm trying to figure how options will move in different scenarios. Is there any way to get an idea of what will happen.

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The delta of the option tells you exactly this. But also realize volatility changes, and time decay can offset these changes as well.

ie, a $17 option for silver might have a delta of 30 3 months out. So a $1.50 move in silver would change the option's value by $.45. Also realize delta changes as it gets closer to the money; that is what gamma tells.

My standard answer:
The CBOE, redoption, and optionscentral websites have a lot of info. Also you can download thinkorswim software and use their Analyze page to graph out various scenarios. Natenberg and McMillian are a couple must reads.
My advice is for you not to trade options until you are equipped and prepared to do so.
Two choices if you must trade options: learn everything about them over the next couple years before putting any significant money in them, or end up eventually losing your money to the pros.

Here is what you need to know, if all you do is go long calls or puts.

1) They can move a lot in relation to the underlying.

2) They lose time value.

You want to buy a call at the beginning of a large upward move in the underlying asset. For example you could have bought the NDX 1900 call this morning for $400 and sold it a few hours later for $900. Unless the NDX opens on Friday 4/18 above 1900 that option will expire worthless.

For example if silver is at 12.82 with three months to expiration I buy a call $4 away from the money how much will this option increase if the price of silver increase by $3.

Or how much will the price of an option increase if silver jumps $1.50 in one week.

I'm trying to figure how options will move in different scenarios. Is there any way to get an idea of what will happen.

More...

You can check the option table to see how much the option price changes relative to the change in price, for a 12.82$ value I believe it would be around $1.5 for $3 increased or better. For options, you typically want to buy at least 3 months away or more, the longer the cheaper but it will be harder to predict. As time value expires the intrinsic value will go to zero, so you'd want to sell the option 1 month before expiration date. Besides time value, there are earning report and news... that could also affect the option prices; so it's good to sell the option early while you can, don't hold on untill the end. Some last notes, read the news everyday so you'll know if the stock is up for sale; you'd have to get out right away or it might go to zeroand stay away from market beween dec to feb, it's slow.

You can check the option table to see how much the option price changes relative to the change in price, for a 12.82$ value I believe it would be around $1.5 for $3 increased or better. For options, you typically want to buy at least 3 months away or more, the longer the cheaper but it will be harder to predict. As time value expires the intrinsic value will go to zero, so you'd want to sell the option 1 month before expiration date. Besides time value, there are earning report and news... that could also affect the option prices; so it's good to sell the option early while you can, don't hold on untill the end. Some last notes, read the news everyday so you'll know if the stock is up for sale; you'd have to get out right away or it might go to zeroand stay away from market beween dec to feb, it's slow.